The Liverpudlian is the third longest-serving manager in the football pyramid behind Sir Alex Ferguson and Arsene Wenger, and should the Bantams wish to continue their interest, Coleman could leave without any compensation being paid to the Reds.
Chief Executive Robert Heys said: "We have had no official approach from Bradford for the services of John Coleman.
"We are on a fantastic run so it comes as no surprise to us that he is being linked with a possible move away from the club.
"However, I would like to think that John would like to continue and bring to fruition Stanley's promotion hopes this season. We are on a such a good run and it would be a devastating blow to us if he were to leave."